求助PREP里的数学题，谢谢！

baobaoekin

请大家指导一下这几个题，谢谢！

1、         The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the present concentration of chemical B present. The concentration of B is increased 100%, which of the following is closet to the percent change in the concentration of A to keep the reaction rate unchanged?

  The answer is increase 40% 怎么得来的？

2.    If m and n are positive integer, what is the remainder when

      3^(4*n +2) is divided by 10?

   (1)n=2      (2)m=1

       为什么是 B？

3.    If x*y=1, 2(x+y)^2/2(x-y)^2=?

   选项2, 4, 8, 16, 32     答案是16，为什么？

4.  Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are D?

   (1) The average salary of the M is 5，000 less than average salary of all employees.

  (2) The average salary of the D is 15，000 greater than average salary of all employees

5. A certain firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (two groups are considered different if at least one group member is different)

     答案是100

ilhht

第一个题目rate：a平方＝rate：1／b所说rate＝a平方＊rate／b，所以说当b增大为原来的2倍的时候，a平方也应当增大为原来的两倍，才能使得rate保持不变。根号2是1.41所以是增加了40％

第二个题目，M在哪里？楼主是不是搞错了？

ilhht

第4个题目，假设M表示manager的个数 D表示director的个人

    

由条件1可以得出：（M总工资＋D总工资）／（M＋D）－M总工资／M＝5000

    

由条件2可以得出：（M总工资＋D总工资）／（M＋D）－D总工资／D＝15000

    

把这两个式子通分，然后化简一下，比如第一个

    

（M总工资＋D总工资）＊M－M总工资＊（M＋D）＝5000＊M＊（M＋D）

    

M总工资＊M＋D总工资＊M－M总工资＊M－M总工资＊D＝5000＊M＊（M＋D）

    

M总工资＊D－D＊总工资M＝5000＊M＊（M＋D）

    

同样的道理，再把第2个式子也化简，得出

    

D＊M总工资－M＊D总工资＝－15000＊D＊（D＋M）

    

然后由这两个化简的式子可以得到M／D的比例是1／3

    

然后进一步可以推出（M＋D）／D＝4／3

    

反过来就是3／4

    

所以可以推出答案，充分性成立

ilhht

最后一个题目：4个seniior6个junior 选3个人，要至少有一个是senior

    

从反面考虑，用总人数减去一个senior也没有的情况，比较好做

    

C（3，10）－C（3，6）＝120－20＝20

另外，楼主，第3个题目好像有问题

希望可以帮到你

baobaoekin

非常非常感谢！